The mean of each dataset tht follows is 62 which dataset is less spread out..justify your answerbusing the mean absolute deviation of each. Dataset round your answer to the nearest tent..data set number 1...51,53, 56,69,72,80
Dataset number 2...49,55,61,63,70,74
To determine which dataset is less spread out, we need to calculate the mean absolute deviation for each dataset.
Dataset 1:
Mean = (51+53+56+69+72+80)/6 = 381/6 = 63.5
Mean absolute deviation = (|51-63.5| + |53-63.5| + |56-63.5| + |69-63.5| + |72-63.5| + |80-63.5|)/6
= (12.5 + 10.5 + 7.5 + 5.5 + 8.5 + 16.5)/6
= 61/6
≈ 10.2
Dataset 2:
Mean = (49+55+61+63+70+74)/6 = 372/6 = 62
Mean absolute deviation = (|49-62| + |55-62| + |61-62| + |63-62| + |70-62| + |74-62|)/6
= (13 + 7 + 1 + 1 + 8 + 12)/6
= 42/6
= 7
Comparing the mean absolute deviations, we see that the dataset with a mean absolute deviation of 7 (dataset 2) is less spread out compared to the dataset with a mean absolute deviation of 10.2 (dataset 1). Therefore, dataset number 2 is less spread out.